{"id":66279,"date":"2018-03-09T22:54:35","date_gmt":"2018-03-09T22:54:35","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/multigraded-structures-and-the-depth-of-blow-up-algebras\/"},"modified":"2018-03-09T22:54:35","modified_gmt":"2018-03-09T22:54:35","slug":"multigraded-structures-and-the-depth-of-blow-up-algebras","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/barcelona\/multigraded-structures-and-the-depth-of-blow-up-algebras\/","title":{"rendered":"Multigraded structures and the depth of blow-up algebras"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Gemma Colome Nin <\/strong><\/h2>\n<p>El objetivo de esta tesis es contribuir al conocimiento de propiedades cohomol\u00f3gicas de m\u00f3dulos multigraduados no-est\u00e1ndar. En particular estudiamos la funci\u00f3n de hilbert de un m\u00f3dulo multigraduado no-est\u00e1ndar, la profundidad asint\u00f3tica de las componentes homog\u00e9neas de un m\u00f3dulo multigraduado y la profundidad asint\u00f3tica de los m\u00f3dulos de veronese. Para ello, generalizamos algunos invariantes cohomol\u00f3gicos en el caso multigraduado no-est\u00e1ndar y estudiamos propiedades de anulaci\u00f3n de m\u00f3dulos de cohomolog\u00eda local. En particular estudiamos la profundidad generalizada de un m\u00f3dulo multigraduado.  un segundo objetivo de la tesis es el estudio de la profundidad de las \u00e1lgebras de blow-up asociadas a un ideal en la tesis se obtienen versiones refinadas de conjeturas sobre la profundidad del anillo graduado asociado a un ideal . Utilizando algunas estructuras bigraduadas, se pueden interpretar los enteros que aparecen en la conjetura de guerrieri y en la conjetura de wang como multiplicidades e m\u00f3dulos bigraduados. En particular hemos podido dar respuesta a una pregunta formulada por a. Guerrieri y c. Huneke en 1993. Hemos demostrado que dado un ideal i m-primario en un anillo (r,m) local cohen-macaulay de dimensi\u00f3n d>0 con reducci\u00f3n animal j, suponiendo que las longitudes de las componentes homog\u00e9neas del m\u00f3dulo de valabrega-valla de i y j sean menores o iguales que uno, entonces la profundidad del anillo graduado asociado a i es mayor o igual que d-2.  finalmente, el estudio de la funci\u00f3n de hilbert de ciertos subm\u00f3dulos de los m\u00f3dulos bigraduados estudiados, permite probar algunos casos en que la funci\u00f3n de hilbert de un ideal m-primario en un anillo local cohen-macaulay de dimensi\u00f3n 1, es no decreciente.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Multigraded structures and the depth of blow-up algebras<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Multigraded structures and the depth of blow-up algebras <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Gemma Colome Nin <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Barcelona<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 14\/07\/2008<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Joan Elias Garcia<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Santiago Zarzuela armengou <\/li>\n<li>Mar\u00eda Evelina rossi (vocal)<\/li>\n<li>winfried Bruns (vocal)<\/li>\n<li>Santiago Encinas carrion (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Gemma Colome Nin El objetivo de esta tesis es contribuir al conocimiento de propiedades cohomol\u00f3gicas de m\u00f3dulos [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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